Question

1. a fencing company is putting fences around the properties shown on the map. each unit on the map is 1 yard. they need to decide which property has the longest perimeter so they know which will require the most fencing.

a. complete the table with the perimeters of each of the properties. round to the nearest tenth.

property	perimeter (yd)
q
r
t

scale = 1 yard

Explanation:

Step1: Identify coordinates of P

Vertices of P: $(-6, 2), (-4, 7), (-1, 2)$

Step2: Calculate side lengths of P

Use distance formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d_1=\sqrt{(-4+6)^2+(7-2)^2}=\sqrt{4+25}=\sqrt{29}\approx5.4$
$d_2=\sqrt{(-1+4)^2+(2-7)^2}=\sqrt{9+25}=\sqrt{34}\approx5.8$
$d_3=\sqrt{(-1+6)^2+(2-2)^2}=\sqrt{25+0}=5$

Step3: Sum for P's perimeter

$5.4+5.8+5=16.2$

Step4: Identify coordinates of Q

Vertices of Q: $(3, 2), (6, 7), (9, 2), (6, 4)$

Step5: Calculate side lengths of Q

$d_1=\sqrt{(6-3)^2+(7-2)^2}=\sqrt{9+25}=\sqrt{34}\approx5.8$
$d_2=\sqrt{(9-6)^2+(2-7)^2}=\sqrt{9+25}=\sqrt{34}\approx5.8$
$d_3=\sqrt{(6-9)^2+(4-2)^2}=\sqrt{9+4}=\sqrt{13}\approx3.6$
$d_4=\sqrt{(3-6)^2+(2-4)^2}=\sqrt{9+4}=\sqrt{13}\approx3.6$

Step6: Sum for Q's perimeter

$5.8+5.8+3.6+3.6=18.8$

Step7: Identify coordinates of R

Vertices of R: $(-4, -4), (-1, -5), (-3, -8), (-6, -6)$

Step8: Calculate side lengths of R

$d_1=\sqrt{(-1+4)^2+(-5+4)^2}=\sqrt{9+1}=\sqrt{10}\approx3.2$
$d_2=\sqrt{(-3+1)^2+(-8+5)^2}=\sqrt{4+9}=\sqrt{13}\approx3.6$
$d_3=\sqrt{(-6+3)^2+(-6+8)^2}=\sqrt{9+4}=\sqrt{13}\approx3.6$
$d_4=\sqrt{(-4+6)^2+(-4+6)^2}=\sqrt{4+4}=\sqrt{8}\approx2.8$

Step9: Sum for R's perimeter

$3.2+3.6+3.6+2.8=13.2$

Step10: Identify coordinates of T

Vertices of T: $(5, -2), (9, -2), (7, -8)$

Step11: Calculate side lengths of T

$d_1=\sqrt{(9-5)^2+(-2+2)^2}=\sqrt{16+0}=4$
$d_2=\sqrt{(7-9)^2+(-8+2)^2}=\sqrt{4+36}=\sqrt{40}\approx6.3$
$d_3=\sqrt{(7-5)^2+(-8+2)^2}=\sqrt{4+36}=\sqrt{40}\approx6.3$

Step12: Sum for T's perimeter

$4+6.3+6.3=16.6$

Answer:

Property	Perimeter (yd)
Q	18.8
R	13.2
T	16.6